Symmetric Bending of Beams

Size: px
Start display at page:

Download "Symmetric Bending of Beams"

Transcription

1 Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications for strength based design and analysis of symmetric bending of beams. Develop the discipline to visualize the normal and shear stresses in symmetric bending of beams. 6-1

2 6.5 Due to the action of the external moment M z and force P, the rigid plate shown in Fig. P6.5 was observed to rotate by 2 o and the normal strain in bar 1 was found ε 1 = 2000 µ in in. Both bars have an area of cross-section of = 1/2 in 2 and a Modulus of Elasticity of E = 30,000 ksi. Determine the applied moment M z and force P. z y x P 2 in Bar 2 Bar 1 4 in M z 48 in Fig. P

3 Internal Bending Moment M z = yσ xx d σ d xx = 0 bove equations are independent of material model as these equations represents static equivalency between the normal stress on the entire cross-section and the internal moment. The line on the cross-section where the bending normal stress is zero is called the neutral axis. Location of neutral axis is chosen to satisfy σ d xx = 0. Origin of y is always at the neutral axis, irrespective of the material model. 6-3

4 6.8 Steel (E steel = 30,000 ksi) strips are securely attached to a wooden (E wood = 2,000 ksi) beam as shown below. The normal strain at the cross-section due to bending about the z-axis is ε xx = 100 y µ where y is measured in inches, and the dimensions of the cross-section are d =2 in, h W =4 in and h S = (1/8) in. Determine the equivalent internal moment M z. y d Steel h S z Wood h W Steel h S 6-4

5 Theory of symmetric bending of beams Limitations The length of the member is significantly greater then the greatest dimension in the cross-section. We are away from the regions of stress concentration. The variation of external loads or changes in the cross-sectional areas are gradual except in regions of stress concentration. The cross-section has a plane of symmetry. The loads are in the plane of symmetry. The load direction does not change with deformation. The external loads are not functions of time. 6-5

6 Theory objectives: To obtain a formula for the bending normal stress σ xx, and bending shear stress τ xy in terms of the internal moment M z and the internal shear force V y. To obtain a formula for calculation of the beam deflection v(x). The distributed force p(x), has units of force per unit length, and is considered positive in the positive y-direction. Displacements Kinematics 1 External Forces and Moments Strains 4 Equilibrium Internal Forces and Moments Static Equivalency 3 Stresses Material Models 2 6-6

7 Kinematics z y x Original Grid Deformed Grid ssumption 1 ssumption 2 Squashing, i.e., dimensional changes in the y-direction, is significantly smaller than bending. v ε yy = 0 y v = v ( x ) Plane sections before deformation remain plane after deformation. u = u o ψ y y x ψ u o ssumption 3 Plane perpendicular to the beam axis remain nearly perpendicular after deformation. γ xy

8 ssumption 4 B 1 B 2 O C ψ ψ u D 1 D R R - y y Strains are small. B y 1 D 1 ψ bending normal strain ε xx varies linearly with y and has maximum value at either the top or the bottom of the beam. 2 1 d v --- = ( x) is the curvature of the deformed beam and R is the radius R dx 2 of curvature of the deformed beam. Material Model ssumption 5 Material is isotropic. ssumption 6 Material is linearly elastic. ssumption 7 There are no inelastic strains. From Hooke s Law: σ xx tanψ ψ Method I = dv dx B = CD = CD 1 B 1 B ε xx = = B ε xx = Method II y --- R ( R y) ψ R ψ R ψ u = ysin ψ y ψ 2 u ε xx dψ d v = lim = y = y ( x) x 0 x dx dx 2 2 d v ε xx = y ( x) dx 2 2 d v = Eε xx, we obtainσ xx = Ey ( x) dx 2 6-8

9 Location of neutral axis 2 σ d d v xx = 0 or Ey ( x) d or x 2 = 0 Eyd = 0 d ssumption 8 Material is homogenous across the cross-section of the beam. y d = 0 Neutral axis i.e, the origin, is at the centroid of the cross-section constructed from linear-elastic, isotropic, homogenous material. The axial problem and bending problem are de-coupled if the origin is at the centroid for linear-elastic, isotropic, homogenous material bending normal stress σ xx varies linearly with y and is zero at the centroid. bending normal stress σ xx is maximum at a point farthest from the neutral axis (centroid). 6-9

10 6.20 The cross-section of a beam with a coordinate system that has an origin at the centroid C of the cross-section is shown. The normal strain at point due to bending about the z-axis, and the Modulus of Elasticity are as given. (a) Plot the stress distribution across the cross-section. (b) Determine the maximum bending normal stress in the cross-section. (c) Determine the equivalent internal bending moment M z by integration. ε xx = 200 µ E = 8000 ksi z 4 in y C 4 in 1 in 1 in 6-10

11 Sign convention for internal bending moment M z = yσ xx d The direction of positive internal moment M z on a free body diagram must be such that it puts a point in the positive y direction into compression. 6-11

12 Sign convention for internal shear force Internal Forces and Moment necessary for equilibrium Recall ssumption 3: Plane perpendicular to the beam axis remain nearly perpendicular after deformation. γ xy 0. From Hooke s Law: τ xy = Gγ xy Bending shear stress is small but not zero. Check on theory: The maximum bending normal stress σ xx in the beam should be nearly an order of magnitude greater than the maximum bending shear stress τ xy. V y = τ xy d The direction of positive internal shear force on a free body diagram is in the direction of positive shear stress on the surface. 6-12

13 6.26 beam and loading in three different coordinate system is shown. Determine the internal shear force and bending moment at the section containing point for the three cases shown using the sign convention described in Section kn/m 5 kn/m 5 kn/m x x x y 0.5 m 0.5 m 0.5 m 0.5 m 0.5 m y Case 1 Case 2 Case m y 6-13

14 Flexure Formulas σ xx = 2 d v Ey ( x) dx d v d v 2 M z = yσ xx d = y Ey ( x) d x 2 = ( x) Ey d d x 2 d For homogenous cross-sections 2 d v Moment-curvature equation: M z = EI zz 2 d x I zz is the second area moment of inertia about z-axis. The quantity EI zz is called the bending rigidity of a beam cross-section. Flexure stress formula: σ xx = M z y I zz Two options for finding M z On a free body diagram M z is drawn as per the sign convention irrespective of the loading. positive values of stress σ xx are tensile negative values of σ xx are compressive. On a free body diagram M z is drawn at the imaginary cut in a direction to equilibrate the external loads. The tensile and compressive nature of σ xx must be determined by inspection. 6-14

15 6.20 The cross-section of a beam with a coordinate system that has an origin at the centroid C of the cross-section is shown. The normal strain at point due to bending about the z-axis, and the Modulus of Elasticity are as given. (d) Determine the equivalent internal bending moment M z by flexure formula. ε xx = 200 µ E = 8000 ksi z 4 in y C 4 in 1 in 1 in 6-15

16 Class Problem 1 The bending normal stress at point B is 15 ksi. (a) Determine the maximum bending normal stress on the cross-section. (b) What is the bending normal strain at point if E = 30,000 ksi. 6-16

17 6.15 Fig. P6.15(a) shows four separate wooden strips that bend independently about the neutral axis passing through the centroid of each strip. Fig. P6.15(b) shows the four strips are glued together and bend as a unit about the centroid of the glued cross-section. (a) Show that I G = 16I S, where I G is the area moment of inertias for the glued crosssection and I S is the total area moment of inertia of the four separate beams. (b) lso show, where σ G and σ S are the maximum bending normal stress at any cross-section for the glued and separate beams, respectively. (a) σ G = σ S 4 (b) Fig. P

18 6.30 For the beam and loading shown, draw an approximate deformed shape of the beam. By inspection determine whether the bending normal stress is tensile or compressive at points and B. M B Class Problem For the beam and loading shown, draw an approximate deformed shape of the beam. By inspection determine whether the bending normal stress is tensile or compressive at points and B. B 6-18

19 6.41 The beam, loading and the cross-section of the beam are as shown. Determine the bending normal stress at point and the maximum bending normal stress in the section containing point 6-19

20 6.46 wooden (E = 10 GPa) rectangular beam, loading and crosssection are as shown in Fig. P6.46. The normal strain at point in Fig. P6.46 was measured as ε xx = 600 µ. Determine the distributed force w that is acting on the beam. w kn/m 100 mm x 25mm 0.5 m 0.5 m Fig. P

21 Shear and Moment by Equilibrium Differential Beam Element Differential Equilibrium Equations: dv y dx The above equilibrium equations are applicable at all points on the beam except at points where there is a point (concentrated) force or point moment. Two Options for finding V y and M z as a function of x Integrate equilibrium equations and find integration constants by using boundary conditions or continuity conditions. This approach is preferred if p not uniform or linear. Make an imaginary cut at some location x, draw free body diagram and use static equilibrium equations to find V y and M z. Check results using the differential equilibrium equations above. This approach is preferred if p is uniform or linear. = p dm z dx = V y 6-21

22 6.51 (a) Write the equations for shear force and bending moments as a function of x for the entire beam. (b) Show your results satisfy the differential equilibrium equations. y 5 kn/m x 3 m 6-22

23 6.58 For the beam shown in Fig. P6.58, (a)write the shear force and moment equation as a function of x in segment CD and segment DE. (b) Show that your results satisfy the differential equilibrium equations. (c) What are the shear force and bending moment value just before and just after point D. Fig. P6.58 Class Problem 3 Write the shear force and moment equation as a function of x in segment B. 6-23

24 Shear and Moment Diagrams Shear and Moment diagrams are a plots of internal shear force V y and internal bending moment M z vs. x. Distributed force n integral represent area under the curve. To avoid subtracting positive areas and adding negative areas, define V = V y x 2 x 2 V 2 = V 1 + pdx M 2 = M 1 + Vdx x 1 x 1 y x (a) (b) (c) (d) w x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 w V 1 V 2 =V 1 -w(x 2 -x 1 ) V V 2 =V 1 +w(x 2 -x 1 ) V V V x x 1 x 1 x 2 2 V V x 1 1 x 1 2 -V y -V y -V -V y y x x V 2 =V 1 -w(x 2 -x 1 ) 2 V V 1 2 =V 1 +w(x 2 -x 1 ) 1 x Increasing incline of tangent 1 Decreasing incline of tangent Increasing incline of tangent Decreasing incline of tangent M M 2 M 2 1 M z M1 M z M 1 M z M M 1 z M 2 x 1 x 2 x 1 x 2 M 2 x 1 x 2 x 1 x 2 If V y is linear in an interval then M z will be a quadratic function in that interval. Curvature rule for quadratic M z curve. The curvature of the M z curve must be such that the incline of the tangent to the M z curve must increase (or decrease) as the magnitude of the V increases (or decreases). or The curvature of the moment curve is concave if p is positive, and convex if p is negative. 6-24

25 Point Force and Moments Internal shear force jumps by the value of the external force as one crosses the external force from left to right. Internal bending moment jumps by the value of the external moment as one crosses the external moment from left to right. Shear force & moment templates can be used to determine the direction of the jump in V and M z. template is a free body diagram of a small segment of a beam created by making an imaginary cut just before and just after the section where the a point external force or moment is applied. Shear Force Template V 1 V 2 M1 Moment Template M ext M 2 x x x x F ext V 2 = V 1 + F ext M 2 = M 1 + M ext Template Equations The jump in V is in the direction of F ext 6-25

26 6.70 Draw the shear and moment diagram and determine the values of maximum shear force V y and bending moment M z. M1 M ext M 2 x x M 2 = M 1 + M ext 6-26

27 6.77 Two pieces of lumber are glued together to form the beam shown Fig. P6.77. Determine the intensity w of the distributed load, if the maximum tensile bending normal stress in the glue limited to 800 psi (T) and maximum bending normal stress is wood is limited to 1200 psi. w lb / in 2 in 30 in 70 in 4 in 1 in Fig. P

28 Shear Stress in Thin Symmetric Beams Recollect problem 6-15 for motivation for gluing beams I G = 16I S σ G = σ S 4 Separate Beams Glued Beams Relative Sliding No Relative Sliding ssumption of plane section perpendicular to the axis remain perpendicular during bending requires the following limitation. Maximum bending shear stress must be an order of magnitude less than maximum bending normal stress. 6-28

29 Shear stress direction Shear Flow: q = τ xs t The units of shear flow q are force per unit length. The shear flow along the center-line of the cross-section is drawn in such a direction as to satisfy the following rules: the resultant force in the y-direction is in the same direction as V y. the resultant force in the z-direction is zero. it is symmetric about the y-axis. This requires shear flow will change direction as one crosses the y-axis on the center-line. 6-29

30 6.88 ssuming a positive shear force V y, (a) sketch the direction of the shear flow along the center-line on the thin cross-sections shown.(b) t points, B, C, and D, determine if the stress component is τ xy or τ xz and if it is positive or negative. y B D z C Class Problem ssuming a positive shear force V y, (a) sketch the direction of the shear flow along the center-line on the thin cross-sections shown.(b) t points, B, C, and D, determine if the stress component is τ xy or τ xz and if it is positive or negative. B y D z C 6-30

31 Bending Shear Stress Formula ( N s + d N s ) N s s is the area between the free surface and the point where shear stress is being evaluated. Define: ssumption 9 + τ sx tdx = 0 τ sx t d τ sx t σ dx d d = xx = d dx = Q z s = τ sx t s = yd s The beam is not tapered. M z y d dx I zz M z Q z I zz = dn s dx d dx M z yd I zz s Q z dm q tτ sx z Q z V y V y Q = = = z τ I zz dx I zz sx = τ xs = I zz t 6-31

32 Calculation of Q z Q z = yd s is the area between the free surface and the point where shear stress is being evaluated. Q z is zero at the top surface as the enclosed area s is zero. Q z is zero at the bottom surface ( s =) by definition of centroid. s z s Line along which Shear stress is being found. Centroid of 2 y Centroid of s Q z s y s y s Neutral xis y 2 Q z = 2 y 2 = 2 Q z is maximum at the neutral axis. Bending shear stress at a section is maximum at the neutral axis. 6-32

33 Bending stresses and strains Top or Bottom Neutral xis Point in Web Point in Flange ε xx γ xy σ xx = ε νσ xx E yy νσ xx = = νε E xx ε zz = = νε E xx τ xy τ = γ xz G xz = G 6-33

34 6.97 For the beam, loading and cross-section shown, determine: (a) the magnitude of the maximum bending normal and shear stress. (b) the bending normal stress and the bending shear stress at point. Point is on the cross-section 2 m from the right end. Show your result on a stress cube. The area moment of inertia for the beam was calculated to be I zz = 453 (10 6 ) mm

35 Shear Flow q = V y Q z I zz s s V F s V F P q = V F s q = 2V F s 6-35

36 6.104 wooden cantilever box beam is to be constructed by nailing four 1 inch x 6 inch pieces of lumber in one of the two ways shown. The allowable bending normal and shear stress in the wood are 750 psi and 150 psi, respectively. The maximum force that the nail can support is 100 lbs. Determine the maximum value of load P to the nearest pound, the spacing of the nails to the nearest half inch, and the preferred nailing method.* Joining Method 1 Joining Method

37 6.115 cantilever, hollow-circular aluminum beam of 5 feet length is to support a load of 1200-lbs. The inner radius of the beam is 1 inch. If the maximum bending normal stress is to be limited to 10 ksi, determine the minimum outer radius of the beam to the nearest 1/16th of an inch. 6-37

M. Vable Mechanics of Materials: Chapter 5. Torsion of Shafts

M. Vable Mechanics of Materials: Chapter 5. Torsion of Shafts Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

More information

Torsion of Shafts Learning objectives

Torsion of Shafts Learning objectives Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

More information

[8] Bending and Shear Loading of Beams

[8] Bending and Shear Loading of Beams [8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight

More information

MECE 3321: Mechanics of Solids Chapter 6

MECE 3321: Mechanics of Solids Chapter 6 MECE 3321: Mechanics of Solids Chapter 6 Samantha Ramirez Beams Beams are long straight members that carry loads perpendicular to their longitudinal axis Beams are classified by the way they are supported

More information

Mechanical Properties of Materials

Mechanical Properties of Materials Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

More information

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

More information

BEAM DEFLECTION THE ELASTIC CURVE

BEAM DEFLECTION THE ELASTIC CURVE BEAM DEFLECTION Samantha Ramirez THE ELASTIC CURVE The deflection diagram of the longitudinal axis that passes through the centroid of each cross-sectional area of a beam. Supports that apply a moment

More information

7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses

7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses 7 TRANSVERSE SHEAR Before we develop a relationship that describes the shear-stress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within

More information

Lecture 15 Strain and stress in beams

Lecture 15 Strain and stress in beams Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

More information

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly

Consider an elastic spring as shown in the Fig.2.4. When the spring is slowly .3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original

More information

Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics)

Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Week 7, 14 March Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Ki-Bok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear

More information

3. BEAMS: STRAIN, STRESS, DEFLECTIONS

3. BEAMS: STRAIN, STRESS, DEFLECTIONS 3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets

More information

NAME: Given Formulae: Law of Cosines: Law of Sines:

NAME: Given Formulae: Law of Cosines: Law of Sines: NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.

More information

Properties of Sections

Properties of Sections ARCH 314 Structures I Test Primer Questions Dr.-Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body

More information

Example 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.

Example 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60. 162 3. The linear 3-D elasticity mathematical model The 3-D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides

More information

CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES

CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric

More information

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3. ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on

More information

Samantha Ramirez, MSE

Samantha Ramirez, MSE Samantha Ramirez, MSE Centroids The centroid of an area refers to the point that defines the geometric center for the area. In cases where the area has an axis of symmetry, the centroid will lie along

More information

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the

More information

CHAPTER 4: BENDING OF BEAMS

CHAPTER 4: BENDING OF BEAMS (74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are

More information

Stress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 4 ME 76 Spring 017-018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a

More information

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd Chapter Objectives To generalize the procedure by formulating equations that can be plotted so that they describe the internal shear and moment throughout a member. To use the relations between distributed

More information

ENG2000 Chapter 7 Beams. ENG2000: R.I. Hornsey Beam: 1

ENG2000 Chapter 7 Beams. ENG2000: R.I. Hornsey Beam: 1 ENG2000 Chapter 7 Beams ENG2000: R.I. Hornsey Beam: 1 Overview In this chapter, we consider the stresses and moments present in loaded beams shear stress and bending moment diagrams We will also look at

More information

Samantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2

Samantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2 Samantha Ramirez, MSE Stress The intensity of the internal force acting on a specific plane (area) passing through a point. Δ ΔA Δ z Δ 1 2 ΔA Δ x Δ y ΔA is an infinitesimal size area with a uniform force

More information

Bending Stress. Sign convention. Centroid of an area

Bending Stress. Sign convention. Centroid of an area Bending Stress Sign convention The positive shear force and bending moments are as shown in the figure. Centroid of an area Figure 40: Sign convention followed. If the area can be divided into n parts

More information

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 1

MECE 3321 MECHANICS OF SOLIDS CHAPTER 1 MECE 3321 MECHANICS O SOLIDS CHAPTER 1 Samantha Ramirez, MSE WHAT IS MECHANICS O MATERIALS? Rigid Bodies Statics Dynamics Mechanics Deformable Bodies Solids/Mech. Of Materials luids 1 WHAT IS MECHANICS

More information

CHAPTER -6- BENDING Part -1-

CHAPTER -6- BENDING Part -1- Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER -6- BENDING Part -1-1 CHAPTER -6- Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and

More information

CHAPTER 5. Beam Theory

CHAPTER 5. Beam Theory CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions

More information

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)? IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at

More information

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

More information

Solution: The moment of inertia for the cross-section is: ANS: ANS: Problem 15.6 The material of the beam in Problem

Solution: The moment of inertia for the cross-section is: ANS: ANS: Problem 15.6 The material of the beam in Problem Problem 15.4 The beam consists of material with modulus of elasticity E 14x10 6 psi and is subjected to couples M 150, 000 in lb at its ends. (a) What is the resulting radius of curvature of the neutral

More information

6. Bending CHAPTER OBJECTIVES

6. Bending CHAPTER OBJECTIVES CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where

More information

Advanced Structural Analysis EGF Section Properties and Bending

Advanced Structural Analysis EGF Section Properties and Bending Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear

More information

7.4 The Elementary Beam Theory

7.4 The Elementary Beam Theory 7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be

More information

PES Institute of Technology

PES Institute of Technology PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject

More information

7.3 Design of members subjected to combined forces

7.3 Design of members subjected to combined forces 7.3 Design of members subjected to combined forces 7.3.1 General In the previous chapters of Draft IS: 800 LSM version, we have stipulated the codal provisions for determining the stress distribution in

More information

CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 2. Discontinuity functions

CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 2. Discontinuity functions 1. Deflections of Beams and Shafts CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 1. Integration method. Discontinuity functions 3. Method

More information

Name (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM

Name (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Name (Print) (Last) (First) Instructions: ME 323 - Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Circle your lecturer s name and your class meeting time. Gonzalez Krousgrill

More information

5. What is the moment of inertia about the x - x axis of the rectangular beam shown?

5. What is the moment of inertia about the x - x axis of the rectangular beam shown? 1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment

More information

Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004

Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004 Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. 1. A beam is loaded as shown. The dimensions of the cross section appear in the insert. the figure. Draw a complete free body diagram showing an equivalent

More information

[5] Stress and Strain

[5] Stress and Strain [5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law

More information

Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee

Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Lecture - 28 Hi, this is Dr. S. P. Harsha from Mechanical and

More information

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.

ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft. ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2

More information

CHAPTER 6: Shearing Stresses in Beams

CHAPTER 6: Shearing Stresses in Beams (130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.

More information

FINAL EXAMINATION. (CE130-2 Mechanics of Materials)

FINAL EXAMINATION. (CE130-2 Mechanics of Materials) UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,

More information

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

More information

CIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:

CIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR: MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine

More information

Unit 13 Review of Simple Beam Theory

Unit 13 Review of Simple Beam Theory MIT - 16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 10-15 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics

More information

Tuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE

Tuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE 1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for

More information

MECE 3321: MECHANICS OF SOLIDS CHAPTER 5

MECE 3321: MECHANICS OF SOLIDS CHAPTER 5 MECE 3321: MECHANICS OF SOLIDS CHAPTER 5 SAMANTHA RAMIREZ TORSION Torque A moment that tends to twist a member about its longitudinal axis 1 TORSIONAL DEFORMATION OF A CIRCULAR SHAFT Assumption If the

More information

PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK

PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM - 613 403 - THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310

More information

ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING

ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING QUESTION BANK FOR THE MECHANICS OF MATERIALS-I 1. A rod 150 cm long and of diameter 2.0 cm is subjected to an axial pull of 20 kn. If the modulus

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

UNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded

More information

Steel Cross Sections. Structural Steel Design

Steel Cross Sections. Structural Steel Design Steel Cross Sections Structural Steel Design PROPERTIES OF SECTIONS Perhaps the most important properties of a beam are the depth and shape of its cross section. There are many to choose from, and there

More information

QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS

QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,

More information

Outline. Organization. Stresses in Beams

Outline. Organization. Stresses in Beams Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of

More information

Part 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.

Part 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1. NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:

More information

Mechanics of Structure

Mechanics of Structure S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI

More information

Sub. Code:

Sub. Code: Important Instructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may

More information

M5 Simple Beam Theory (continued)

M5 Simple Beam Theory (continued) M5 Simple Beam Theory (continued) Reading: Crandall, Dahl and Lardner 7.-7.6 In the previous lecture we had reached the point of obtaining 5 equations, 5 unknowns by application of equations of elasticity

More information

Mechanics of Solids notes

Mechanics of Solids notes Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any cross-section of a beam may consists of a resultant normal force,

More information

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion Introduction Stress and strain in components subjected to torque T Circular Cross-section shape Material Shaft design Non-circular

More information

Beams. Beams are structural members that offer resistance to bending due to applied load

Beams. Beams are structural members that offer resistance to bending due to applied load Beams Beams are structural members that offer resistance to bending due to applied load 1 Beams Long prismatic members Non-prismatic sections also possible Each cross-section dimension Length of member

More information

Comb resonator design (2)

Comb resonator design (2) Lecture 6: Comb resonator design () -Intro Intro. to Mechanics of Materials School of Electrical l Engineering i and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory

More information

Mechanics of Materials Primer

Mechanics of Materials Primer Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus

More information

FIXED BEAMS IN BENDING

FIXED BEAMS IN BENDING FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported

More information

Downloaded from Downloaded from / 1

Downloaded from   Downloaded from   / 1 PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their

More information

BEAM A horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam

BEAM A horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam BEM horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam INTERNL FORCES IN BEM Whether or not a beam will break, depend on the internal resistances

More information

UNIT- I Thin plate theory, Structural Instability:

UNIT- I Thin plate theory, Structural Instability: UNIT- I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and in-plane loading Thin plates having

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Please indicate your group number (If applicable) Circle Your Instructor s Name and Section: MWF 8:30-9:20 AM Prof. Kai Ming Li MWF 2:30-3:20 PM Prof. Fabio Semperlotti MWF 9:30-10:20 AM Prof. Jim Jones

More information

Stresses in Curved Beam

Stresses in Curved Beam Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions:

More information

MECHANICS OF MATERIALS. Analysis of Beams for Bending

MECHANICS OF MATERIALS. Analysis of Beams for Bending MECHANICS OF MATERIALS Analysis of Beams for Bending By NUR FARHAYU ARIFFIN Faculty of Civil Engineering & Earth Resources Chapter Description Expected Outcomes Define the elastic deformation of an axially

More information

This procedure covers the determination of the moment of inertia about the neutral axis.

This procedure covers the determination of the moment of inertia about the neutral axis. 327 Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the T-beam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination

More information

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment 7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that

More information

STRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains

STRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains STRENGTH OF MATERIALS-I Unit-1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between

More information

DESIGN OF BEAMS AND SHAFTS

DESIGN OF BEAMS AND SHAFTS DESIGN OF EAMS AND SHAFTS! asis for eam Design! Stress Variations Throughout a Prismatic eam! Design of pristmatic beams! Steel beams! Wooden beams! Design of Shaft! ombined bending! Torsion 1 asis for

More information

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [2910601] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I.

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics

More information

Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements

Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements CIVL 7/8117 Chapter 12 - Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness

More information

4. BEAMS: CURVED, COMPOSITE, UNSYMMETRICAL

4. BEAMS: CURVED, COMPOSITE, UNSYMMETRICAL 4. BEMS: CURVED, COMPOSITE, UNSYMMETRICL Discussions of beams in bending are usually limited to beams with at least one longitudinal plane of symmetry with the load applied in the plane of symmetry or

More information

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the

More information

Solution: The strain in the bar is: ANS: E =6.37 GPa Poison s ration for the material is:

Solution: The strain in the bar is: ANS: E =6.37 GPa Poison s ration for the material is: Problem 10.4 A prismatic bar with length L 6m and a circular cross section with diameter D 0.0 m is subjected to 0-kN compressive forces at its ends. The length and diameter of the deformed bar are measured

More information

Chapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson

Chapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. El-kashif Civil Engineering Department, University

More information

3 Hours/100 Marks Seat No.

3 Hours/100 Marks Seat No. *17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full

More information

R13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PART-A

R13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PART-A SET - 1 II B. Tech I Semester Regular Examinations, Jan - 2015 MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) Time: 3 hours Max. Marks: 70 Note: 1. Question Paper consists of two parts (Part-A and Part-B)

More information

Mechanical Design in Optical Engineering

Mechanical Design in Optical Engineering Torsion Torsion: Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member s longitudinal axis. In other words, the member is loaded

More information

[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21

[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21 [7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is

More information

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State

More information

1 of 12. Given: Law of Cosines: C. Law of Sines: Stress = E = G

1 of 12. Given: Law of Cosines: C. Law of Sines: Stress = E = G ES230 STRENGTH OF MATERIALS FINAL EXAM: WEDNESDAY, MAY 15 TH, 4PM TO 7PM, AEC200 Closed book. Calculator and writing supplies allowed. Protractor and compass required. 180 Minute Time Limit You must have

More information

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002 REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS Third E CHAPTER 6 Shearing MECHANCS OF MATERALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University Stresses in Beams and Thin- Walled Members Shearing

More information

Chapter 5 Structural Elements: The truss & beam elements

Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations

More information

Sample Question Paper

Sample Question Paper Scheme I Sample Question Paper Program Name : Mechanical Engineering Program Group Program Code : AE/ME/PG/PT/FG Semester : Third Course Title : Strength of Materials Marks : 70 Time: 3 Hrs. Instructions:

More information

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

twenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete

More information

Mechanics of Materials

Mechanics of Materials Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics

More information